A Phase Field α-navier-stokes Vesicle-fluid Interaction Model: Existence And Uniqueness Of Solutions

In this work we analyze a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction associated to the dynamics of an elastic vesicle immersed in a moving incompressible viscous fluid. This system of equations couples an equation for a phase field variable, used to determine the position of vesicle membrane deformed by the action of the fluid, to the α-Navier- Stokes equations with an extra nonlinear interaction term. We prove global in time existence and uniqueness of solutions for this system in suitable functional spaces even in the three-dimensional case.202397422Adams, R.A., Fournier, J.J.F., (2003) Sobolev Spaces, , 2nd edition, Elsevier/Academic Press, AmsterdamAbkarian, M., Lartigue, C., Viallat, A., Tank treading and unbinding of deformable vesicles in shear flow: Determination of the lift force (2002) Phys. Rev. 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